Derangements and Euler's difference table for $C_\ell\wr S_n$

Details Derangements and Euler's difference table for $C_\ell\wr S_n$ Derangements and Euler's difference table for $C_\ell\wr S_n$

2008-10-15

arxiv.org/abs/0810.2727v1

The Electronic Journal of Combinatorics 15 (2008); #R65

Mathematics

Combinatorics

22 pages

Scientific paper

Euler's difference table associated to the sequence $\{n!\}$ leads naturally to the counting formula for the derangements. In this paper we study Euler's difference table associated to the sequence $\{\ell^n n!\}$ and the generalized derangement problem. For the coefficients appearing in the later table we will give the combinatorial interpretations in terms of two kinds of $k$-successions of the group $C_\ell\wr S_n$. In particular for $\ell=1$ we recover the known results for the symmetric groups while for $\ell=2$ we obtain the corresponding results for the hyperoctahedral groups.

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